Rank-based search operators for learning latent variable models

We derive a Bayesian search algorithm for learning the structure of
latent variable models. This is performed by searching for subsets of
the observed variables whose covariance matrix can be represented as a
sum of a matrix of low rank and a diagonal matrix of residuals. The
resulting search procedure is relatively efficient by using a
variational approximation. The model itself is a generalization of
factor analysis and its variations, where we do not constrain the
dependency structure among latents. The resulting models are often
simpler and give a better fit than models where latents are constrained,
e.g., to be independent.